Model Predictive Control

In this paper, we establish last-iterate convergence rates for off-policy actor--critic methods in reinforcement learning. In particular, under a single-loop, single-timescale implementation and a broad class of policy updates, including approximate policy iteration and natural policy gradient methods, we prove the first $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity guarantee for finding an $ε$-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain. This stands in stark contrast to the existing literature, where an $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity is achieved only through nested-loop updates and/or under strong, algorithm-dependent assumptions on the policies, such as uniform mixing and uniform exploration. Technically, to address the challenges posed by the coupled update equations arising from the single-loop implementation, as well as the potentially unbounded iterates induced by off-policy learning, our analysis is based on a coupled Lyapunov drift framework. Specifically, we establish a geometric convergence rate for the actor and an $\tilde{\mathcal{O}}(1/T)$ convergence rate for the critic, and combine the two Lyapunov drift inequalities through a cross-domination property. We believe this analytical framework is of independent interest and may be applicable to other coupled iterative algorithms with unbounded

Biological neural networks (BNNs) have been established as a powerful and adaptive substrate that offer the potential for incredibly energy and data efficient information processing with distinct learning mechanisms. Yet a core challenge to utilizing BNN for neurocomputation is determining the optimal encoding and decoding mechanisms between the traditional silicon computing interface and the living biology. Here, we propose an Embodied Neurocomputation framework as a systems-level approach to this multi-variable optimization encoding/decoding problem. We operationalize this approach through the first large-scale parameter optimization of encoding configurations for a BNN agent performing closed-loop navigation along an odor-style gradient in a simulated grid-world. Despite the relative simplicity of the task, the biological interactions gave rise to a massive multi-combinatorial search space for optimal parameters. By considering how the components of the system are interconnected and parameterized, we evaluated approximately 1,300 parameter combinations, over 4,000 hours of real-time agent-environment interactions, to identify 12 configurations that consistently demonstrated learning across multiple episodes. These configurations achieved significantly higher task performances than optimized silicon-based DQN agents under the same interaction budget. These findings represent an initial step toward robust and scalable goal-oriented learning using BNNs. Our framework establishes a foundation for applying task-driven neurocomputing and supports the development of field-wide benchmarks. In the long term, this work supports the development of hybrid bio-silicon architectures capable of efficient, adaptive and real-time computation, including the potential for robotic control applications.

Wheeled-legged robots hold promise for traversing complex terrains and offer superior mobility compared to legged robots. However, wheeled-legged robots must effectively balance both wheeled driving and legged control. Furthermore, due to noisy proprioceptive sensing and real-world motor constraints, realizing robust and adaptive locomotion at peak performance of motors remains challenging. We propose the Multi-skill Unified Joint Integration of Control Architecture (MUJICA), a unified, fully proprioceptive control framework for wheeled-legged robots that integrates diverse low-level skills-including omnidirectional moving, high platform climbing, and fall recovery-within a single policy. All skills, distinguished by unique indicator variables, are trained jointly with accurate DC-motor constraint modeling. Additionally, a high-level skill selector is learned to dynamically choose the optimal skill based solely on proprioceptions, enabling adaptive responses to the surrounding environment. Therefore, MUJICA enhances sim-to-real robustness and enables seamless transitions across diverse locomotion modes, facilitating autonomous adjustment to the environment. We validate our framework in both simulation and real-world experiments on the Unitree Go2-W robot, demonstrating significant improvements in adaptability and task success in unstructured environments.

This paper addresses the problem of estimating the relative pose (position and orientation) and velocity of a vehicle with respect to a moving target, where both are equipped with Inertial Measurement Units (IMUs), assuming the availability of relative position or bearing measurements. The body-target relative dynamics are formulated on $\mathbf{SE}_2(3)$ and recast into a linear time-varying (LTV) model in the ambient space $\mathbb{R}^{15}$, on which a deterministic Riccati observer is designed. We analyze the uniform observability (UO) conditions required to guarantee global exponential convergence of the estimation error in the ambient space for both measurement cases. In the case of relative position measurements, UO requires only a persistence-of-excitation condition on the target acceleration, whereas for bearing measurements, additional conditions are required. Building on this, a nonlinear complementary filter on $\mathbf{SO}(3)$ is designed to provide a smooth estimate of the orientation component of the state with almost global asymptotic stability. Finally, simulation results are provided to validate the proposed solution.

In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a certified backup policy to ensure safety. To handle arbitrary uncertainties from ambiguous distributions, i.e., where the distribution is not of specific structure and the true distribution is unknown, we adopt a distributionally robust (DR) formulation using Wasserstein ambiguity sets. Rather than solving a high-dimensional DR trajectory optimization problem online, we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold. We validate our method through simulations across three systems, from a Dubins vehicle to a high-speed racing car and a fighter jet, demonstrating the broad applicability and computational efficiency.

We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditioner update. For stochastic smooth convex optimization, we prove convergence in expectation under an admissible stepsize condition that can always be satisfied by a conservative spectral bound, without imposing global monotonicity on the second-moment sequence. To obtain a less conservative practical rule, we introduce a computable trace-ratio stepsize, motivated by a local coordinatewise alignment condition. The same structural update is also tested beyond the convex setting with simplified parameters. Experiments validate the predicted stochastic decay and show competitive training performance against Adam and AdamW on deep learning tasks.

Modeling concentric tube robots (CTRs) involves complex nonlinear continuum mechanics, and despite recent progress, physics-based models often lack an accurate representation of the experimental setups. To overcome these limitations, deep neural network-based models have been explored as alternatives with superior accuracy; however, they often overlook known mechanics, require large training datasets, and typically discard shape estimation of the robot. We present a physics-informed neural network (PINN) for kinematic modeling of a 6-DoF CTR with three pre-curved tubes that embeds the Cosserat rod differential equations and learns from few-shot observational data, balancing physics priors with data-driven fitting. PINN enables full-state estimation of shape, twist angle, torsional strain, bending moment, and orientation. Benchmark tests show a mean shape error below 1% of the robot length and accurately recovered other kinematic states, outperforming a purely physics-based Cosserat rod model baseline while using a minimal training set. The resulting model is also computationally efficient and robust, making it well-suited for real-time control applications.

As autonomous vehicles move from a simplified research setting to practical use, there exists a large gap between the dynamic behavior of a human driving and an autonomous system. Risk-aware behavior needs to naturally develop in order to scale to the demands of the real world. A major issue for risk-aware planning and control has been predicting how dynamical uncertainty evolves through time and optimizing plans that account for this without being overly conservative. Here, we present a learning framework to predict distributional dynamics that can be optimized in real time for Model Predictive Control (MPC). We explore the importance of structure when learning distributional dynamics for use in MPC. A rigorous ablation study is conducted on a large dataset of real world off-road driving that shows the impact of deviations from our proposed structure. Furthermore, we deploy our learned model and planning stack on a full sized vehicle in challenging off-road conditions. Our planning architecture is able to naturally regulate the speed of the vehicle based on the environment and consistently demonstrates intelligent behavior over miles of diverse terrain.

In this paper, we study grant-free, asynchronous control-to-control (C2C) communications in an indoor scenario with a shared wireless channel. Each communication node transmits command units, each consisting of a variable-length low-density parity-check (LDPC)--coded payload preceded by a start sequence and followed by a tail sequence. Due to the asynchronous nature of the access, transmissions from different nodes are not aligned over time. As a result, each receiving controller observes the superposition of multiple command units transmitted by different nodes over a receiver-defined superframe interval. Each node transmits one or more replicas of the same command unit. We propose a receiver architecture in which the detection of command unit boundaries (start/tail sequences) is carried out by a single convolutional neural network (CNN) operating directly on the received signal. We show that, while start-sequence detection must rely only on the received waveform, tail-sequence detection can additionally exploit the soft information produced by the LDPC decoder, together with channel estimates. Finally, once commands units are successfully decoded, successive interference cancellation (SIC) can be applied. Simulation results demonstrate that the receiver we propose achieves reliable packet-boundary identification and a low end-to-end packet loss rate, even under uncoordinated and high-traffic operating conditions.

Safe reinforcement learning (RL) typically asks $\textit{what}$ an agent should do. We ask $\textit{when}$ it needs to act, and show that a single policy can jointly learn control inputs and communication-efficient timing decisions under a pointwise Lyapunov safety shield. We focus on stabilization around a known equilibrium, where CARE-based LQR backups, Lyapunov certificates, and classical Lyapunov-STC are well defined, enabling clean comparison against analytical baselines. A run-time assurance (RTA) layer overrides the policy via a one-step-ahead Lyapunov prediction and a precomputed LQR backup, providing a strictly stronger guarantee than constrained MDP methods that enforce safety only in expectation. On an inverted pendulum, cart--pole, and planar quadrotor, the learned policy achieves $1.91\times$, $1.45\times$, and $3.51\times$ higher mean inter-sample interval (MSI) than a Lyapunov-triggered baseline; a fixed LQR controller at the same average rate is unstable on all three plants, showing that adaptive timing, not a lower average rate, makes sparsity safe. A CARE-derived Lyapunov reward transfers across environments without redesign, with a single weight $w_c$ controlling the stability--communication tradeoff; ablations confirm the RTA shield is essential, with its removal reducing MSI by $1.27$--$1.84\times$ and degrading state norms. A preference-conditioned extension recovers the full tradeoff frontier from one model at $\tfrac{2}{11}$ of training compute, and SAC experiments show the results are algorithm-agnostic across discrete and continuous domains. A 12-state 3D quadrotor case study extends the framework to higher-dimensional systems where classical STC is intractable, and robustness to $\pm30\%$ mass variation and disturbances shows graceful degradation, with the RTA absorbing what the learned policy cannot.

Generative agents have proven to be powerful assistants in a wide variety of contexts. Given this success, users are now deploying agents with minimal restrictions in open ended, multi-agent environments. Current methods for monitoring the dynamics of open-ended multi-agent systems are limited to qualitative inspection. In this paper, we extend the process-theoretic notion of adaptive control charts to multi-agent systems to enable automated monitoring. Using simulation, we demonstrate that adaptive control charts are necessary for monitoring multi-agent systems that can learn from their environment. We further demonstrate, both empirically and theoretically, that adaptive control charts are susceptible to adversarial agents that defect sufficiently slowly. These results illustrate a fundamental tradeoff in multi-agent system control: either agents in a system cannot learn or the system is susceptible to adversaries.

Decentralized collision avoidance remains challenging, particularly when agents do not communicate any information related to planned trajectories. Most existing approaches either rely on conservative coordination mechanisms or provide limited guarantees on recursive feasibility and convergence. This paper develops a decentralized contingency MPC framework for multi-agent systems with nonlinear dynamics that achieves collision-free motion under a state-only information pattern. Each agent follows the same consensual rule set, enabling safe decentralized planning without communication. Each agent solves a local optimization problem that couples a nominal trajectory with a contingency certificate ensuring a feasible backup maneuver under receding-horizon operation. A novel geometric and decentralized safe-set update mechanism prevents feasibility loss between consecutive time steps. The resulting scheme guarantees recursive feasibility, including collision avoidance, and establishes a Lyapunov-type convergence result to an admissible safe equilibrium. Simulation results demonstrate performance in both sparse and dense multi-agent environments, including cluttered bottleneck scenarios and under plug-and-play operation.

Model Predictive Control (MPC) is widely used to operate safety-critical infrastructure by predicting future trajectories and optimizing control actions. However, nonlinear dynamics, hard safety constraints, and numerical optimization often render individual control moves opaque to human operators, undermining trust and hindering deployment. This paper presents Hierarchical Causal Abduction (HCA), which combines (i) physics-informed reasoning via domain knowledge graphs, (ii) optimization evidence from Karush--Kuhn--Tucker (KKT) multipliers, and (iii) temporal causal discovery via the PCMCI algorithm to generate faithful, human-interpretable explanations for control actions computed by nonlinear MPC. Across three diverse control applications (greenhouse climate, building HVAC, chemical process engineering) with expert validation, HCA improves explanation accuracy by 53% over LIME (0.478 vs. 0.311) using a single set of cross-domain parameters without per-domain tuning; domain-specific KKT-threshold calibration over 2--3 days further increases accuracy to 0.88. Ablation studies confirm that each evidence source is essential, with 32--37% accuracy degradation when any component is removed, and HCA's ranking-and-validation methodology generalizes beyond MPC to other prediction-based decision systems, including learning-based control and trajectory planning.

We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.

Autonomous and safe navigation of tractor-trailer systems requires accurate, real-time collision avoidance and dynamically feasible control, particularly in cluttered and complex agricultural environments. This is challenging due to their articulated, deformable geometries and nonlinear dynamics. Traditional methods oversimplify vehicle geometry or rely on precomputed distance fields that assume a known map, limiting their applicability in dynamic, partially unknown environments. To address these limitations, we propose a geometric neural encoder that provides fast and accurate distance estimates between the full tractor-trailer body and raw LiDAR perception, enabling real-time, map-free geometric reasoning. These learned distances are integrated into a Model Predictive Path Integral (MPPI) controller, allowing the system to incorporate true articulated geometry directly into its cost evaluation and enabling more responsive navigation in challenging agricultural settings. Simulation results demonstrate that the proposed framework generates dynamically feasible and safe trajectories for navigating tractor-trailer systems in cluttered and complex environments.

This paper proposes a safe data-driven control framework for nonlinear systems with partially known dynamics. The method ensures stability and constraint satisfaction during online learning, assuming only a stabilizable linear approximation of the process is available. Unmodeled nonlinear dynamics are captured by a Gaussian process residual learned in real time. Safety is enforced through a probabilistic control-invariant set derived from Lyapunov theory, guaranteeing high-probability stability. A convex quadratic program computes control inputs that maximize information gain while respecting probabilistic safety constraints. The framework provides finite-sample safety guarantees and allows adaptive expansion of the invariant set as uncertainty decreases. Numerical results validate the approach, demonstrating safe and informative exploration under model uncertainty: the safe set expands by about 30% while the Gaussian process root-mean-square error drops from 1.11 to 0.03.

Training neural networks to satisfy universal constraints over continuous domains poses unique challenges. Common examples include Lyapunov Neural Networks (Lyapunov NNs) and Physics-Informed Neural Networks (PINNs), where analytical solutions are generally either unavailable or overly restrictive. Sample-based methods are therefore commonly used to enforce these constraints, and the choice of samples has a substantial impact on convergence speed, stability, and solution quality. Most existing methods rely on fixed heuristics or handcrafted rules, and are suboptimal in practice. In this paper, we aim to improve upon them by learning, from data and experience, how to dynamically and iteratively adjust the samples in response to the model's evolving learning performance. Trained by reinforcement learning, the learned policy improves empirical constraint satisfaction on test problems while significantly improving efficiency. We validate the approach on both Lyapunov NNs and PINNs, and demonstrate its broader applicability to domains where adaptive input selection is essential for effective training.

Koopman operator theory provides a powerful framework for representing nonlinear dynamics through a linear operator acting on lifted observables, enabling the use of linear control techniques for nonlinear systems. However, Koopman models are typically learned from data and often degrade in performance under model uncertainty and distributional shifts between training and deployment. Although several works have explored online adaptation to address this issue, many rely on neural network-based updates that introduce significant computational overhead and lack formal safety guarantees, limiting their suitability for real-time and safety-critical robotic applications. In this work, we propose a unified framework for continual adaptive Koopman learning that enables safe and efficient online refinement of learned models during task execution. An autoencoder-based Koopman model is first learned offline and subsequently refined online through a contractive adaptation law, which provides theoretical convergence guarantees under distributional shifts and model uncertainty. To improve data efficiency and accelerate model refinement, the adaptation mechanism is integrated with an active learning strategy that drives the system to collect informative data while accomplishing task objectives. The resulting control problem is formulated as a nonconvex optimization problem incorporating both active learning objectives and safety constraints. We further derive theoretical bounds on model approximation error and show how these bounds can be incorporated within a robust Model Predictive Control (MPC) framework to provide formal safety guarantees. The proposed approach unifies learning, excitation, and safety within a single control framework without sacrificing real-time feasibility. Extensive simulation and experimental studies demonstrate superior performance compared to state-of-the-art baselines.

Trajectory optimization for autonomous vehicles usually relies on the kinematic bicycle model because of its computational simplicity. However, when the planned trajectory is executed under the true vehicle dynamics, which include lateral slip, tire stiffness and yaw-lateral coupling, safety constraints can be violated owing to the model mismatch. In this paper, we make three theoretical contributions. First, we derive a characteristic speed $v_c=\sqrt{C_αL/M}$ which separates two different mismatch regimes: below $v_c$ the dynamic bicycle initially oversteers inward (safe); above $v_c$ it understeers outward (safety-critical). Second, we prove that the peak outward deviation $\varepsilon^*$ follows a $T^2$ horizon scaling whose coefficient transitions between a transient bound $\frac{1}{2}(v^2-v_c^2)κ$ and a steady-state bound. Third, we obtain a simulation-free analytical coefficient $a_2^{\mathrm{anal}}=\frac{1}{2}(1-v_c^2/v_{\max}^2)T^2$ that is computable from vehicle parameters and the planning horizon alone. Putting these together, we propose Mismatch-Aware Adaptive Constraint Tightening (MACT), $ε(v,κ)=a_2 v^2|κ|$, which replaces a fixed worst-case margin by a state-dependent one that is large at high speed/curvature but nearly zero on gentle paths. Eight numerical experiments confirm the scaling laws. MACT reaches 100% safety with 84% less wasted margin than a fixed-margin baseline on the 2-DOF vehicle, extends to a nonlinear leaning bicycle, and in a closed-loop direct-shooting MPC comparison it cuts the applied margin by 34% compared with tube MPC while keeping the same safety.

Decentralized federated learning (FL) is a promising approach for training machine learning models on sensor networks, Internet of Things (IoT) devices, and other edge systems where no central server exists. While federated learning offers advantages such as preserving data privacy, it often suffers from non-independent and identically distributed (IID) data distributions across devices, which cause significant performance degradation. This issue is particularly severe when directly optimizing model parameters, because neural network training is inherently non-convex and standard convergence guarantees for convex optimization do not apply. Unlike existing decentralized FL methods that primarily operate in parameter space, we propose federated function-space alternating direction method of multipliers (FedF-ADMM). FedF-ADMM exploits the convexity of loss functionals within function space to derive alternating direction method of multipliers (ADMM)-based update directions, which are subsequently projected onto the parameter space via knowledge distillation. We further introduce a stabilization coefficient to enhance robustness under severe non-IID settings and analyze its behavior from a control-theoretic perspective by interpreting it as a proportional-integral (PI) term. Experiments under challenging non-IID scenarios, including settings where each device has data from only a single label, demonstrate that FedF-ADMM achieves faster and more stable convergence than existing decentralized FL methods, while attaining higher accuracy and better consensus among devices.

We consider a mutual information (MI) regularized version of optimal density control of a discrete-time linear system. MI optimal control has been proposed as an extension of maximum entropy optimal control to trade off between control performance and benefits provided by stochastic inputs. MI regularization induces stochasticity in the policy, which poses challenges for applications of MI optimal control in safety-critical scenarios. To remedy this situation, we impose Gaussian density constraints at specified times to directly control state uncertainty. For this MI optimal density control problem, we propose an alternating optimization algorithm and derive the closed form of each step in the algorithm. In addition, we reveal that the alternating optimization of the MI optimal density control problem coincides with that of the so-called generalized Schrödinger bridge problem associated with the discrete-time linear system.

We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in $\ell_1$-regularized convex programs. From strong convexity and Lagrangian duality, we derive certificates that \emph{safely} discard constraints and decision variables while guaranteeing that all removed constraints remain satisfied and all removed variables are null. To further accelerate the proposed algorithm, we propose a transformer-based deep neural network to guide the dual certificate inference. We validate SHIELD on stochastic model predictive control (SMPC) in complex, multi-modal traffic scenarios, comparing against a full-dimensional SMPC policy. Numerical simulations demonstrate order-of-magnitude computational speedups while preserving feasibility and closed-loop safety, highlighting the practicality of certifiably safe, lightweight MPC in complex driving scenes.

Contact-implicit trajectory optimization (CITO) has attracted growing attention as a unified framework for planning and control in contact-rich robotic tasks. Recent approaches have demonstrated promising results in manipulation and locomotion without requiring a prescribed contact-mode schedule. It is well known that the underlying mathematical programs with complementarity constraints (MPCCs) remain numerically ill-conditioned, and systematic, scalable solution strategies for CITO remain an active area of research. More efficient and principled solvers that can handle contact constraints are therefore essential to broaden the applicability of CITO. In this work, we develop an augmented-Lagrangian approach to CITO for solving MPCC-based CITO with stationarity guarantees. The method can be interpreted as identifying the implicit contact-mode branches on the fly during the trajectory optimization (TO) iterations; we call this approach IMPACT (IMPlicit contact ACtive-set Trajectory optimization). We provide an efficient C++ implementation tailored to trajectory-optimization workloads and evaluate it on the open-source CITO and contact-implicit model predictive control (CI-MPC) benchmarks. On CITO, IMPACT achieves 2.9x-70x speedups over strong baselines (geometric mean 13.8x). On CI-MPC, we show improved control quality for contact-rich trajectories on dexterous manipulation tasks in simulation. Finally, we demonstrate the proposed method on real robotic hardware on a T-shaped object pushing task.

We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $β$-smooth and $γ$-strongly convex regime. Classical analyses of uniform stability, such as the work of Hardt, Recht, and Singer for stochastic gradient descent (SGD), rely on direct coupling arguments and case-by-case control of iterate differences under random sampling. Extending such arguments to accelerated methods, such as Nesterov Accelerated Gradient (NAG), is complicated by the presence of higher-order state dynamics induced by momentum. We first extend this classical approach with the use of Lyapunov functions to provide a uniform stability bound for smooth quadratic NAG, and supplement this result with small-scale numerical experiments. We then extend this framework by modeling first-order accelerated optimizers as Lur'e-type feedback interconnections between a linear dynamical system and a (non-linear) gradient operator. $β$-Smoothness and $γ$-strong convexity are encoded a sector IQC inequality. Under this representation, uniform stability is certified via the existence of a quadratic Lyapunov function satisfying a finite-dimensional linear matrix inequality (LMI) in the form of a feasibility problem, which can be solved via semi-definite programming (SDP). We instantiate this framework for NAG and show how classical uniform stability bounds can be recovered via this framework. These results underscore a structural connection between optimization dynamics and robust control theory, providing a modular methodology for reliable and reproducible numerical certification of uniform stability and generalization behavior of first-order methods via convex optimization tools that is adaptable to increasingly complex optimization algorithms.

Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems governed by partial differential equations (PDEs), but standard PINN training typically relies on soft penalty formulations that combine PDE residuals, data mismatch, and initial/boundary conditions using manually chosen weights. This often leads to ill-conditioning, sensitivity to loss weights, and poor constraint satisfaction. In this work, we reformulate PINN training as an equality-constrained optimization problem and propose a novel Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN (AdamFLIP). The key idea is to view the constraint residuals as the output of a controlled dynamical system and to compute the Lagrange multiplier as a feedback input that locally drives these residuals toward stable linear contraction dynamics. AdamFLIP then applies Adam-style first- and second-moment adaptation to the resulting feedback-linearized Lagrangian gradient, combining principled constraint handling with the scalability and robustness of adaptive neural-network optimization. We test AdamFLIP on a range of benchmark forward and inverse PDE problem, and it consistently outperforms both the standard soft-constrained PINN and state-of-the-art constrained optimizers. Specifically, on the Navier--Stokes equations benchmark, AdamFLIP \textbf{reduces relative $L_2$ error by more than two thirds} for the predicted solution compared to the next best method. Our AdamFLIP framework provides an effective and computationally scalable hard constraint optimization method for PINN training.

Close-proximity offshore wind turbine inspection requires strict clearance control around large cylindrical structures under wind and model mismatch. Nominal Nonlinear Model Predictive Control (NMPC) may violate safety constraints when mass, inertia, thrust effectiveness, drag, or wind conditions differ from nominal assumptions. We propose a sensitivity-based robust NMPC for a tilted multirotor that robustifies the tower-clearance constraint via online constraint tightening. First-order parametric state sensitivities provide a structured-uncertainty margin, while bounded gusts are handled by a stage-dependent additive margin. The formulation augments the nominal NMPC with sensitivity propagation and margin evaluation only, leaving the receding-horizon optimization structure unchanged. Monte-Carlo evaluation over 500 uncertainty realizations on a boundary-critical helical inspection trajectory shows that the proposed controller eliminates the clearance violations observed under nominal NMPC at the cost of a moderate increase in solve time.

We investigate interactive trajectory planning subject to uncertainty in the decisions of surrounding agents. To control the ego-agent, we aim to first learn the decision distribution and solve a Stochastic Model Predictive Control (SMPC) problem. To account for errors in the learned distribution, we show that it is possible to utilize Probably Approximately Correct (PAC) learning in combination with Distributionally Robust (DR) optimization to obtain a solution which accounts for the errors induced by the learning model. The results indicate that our PAC learning-based DR-MPC framework provides a method to interpolate between a robust MPC and an omnipotent SMPC, based on the available number of samples.

Formal verification of neural control barrier functions (NCBFs) remains challenging, especially for neural networks with nonlinear activations like $\tanh$. Existing CROWN-based methods rely on conservative linear relaxations for Jacobian bounds, limiting scalability. We propose LightCROWN, which computes tighter Jacobian bounds by exploiting the analytical properties of activation functions. Experiments on nonlinear control systems including the inverted pendulum, Dubins car, and planar quadrotor demonstrate that LightCROWN improves verification success rates up to 100%, while enhancing speed and scalability. Our approach provides a generalizable improvement for CROWN-based frameworks, enabling more efficient verification of complex NCBFs. The code can be found at github.com/Autonomous-Systems-and-Control-Lab/verify-neural-CBF.

Vision-Language-Action (VLA) models have significantly advanced the capabilities of robotic agents in executing diverse tasks; however, they still face challenges in contact-rich manipulation scenarios that require precise physical interactions. To address this limitation, recent studies have attempted to incorporate tactile signals during downstream tasks, enabling pretrained VLAs to interpret tactile feedback. Nevertheless, introducing new modalities during finetuning, which are rarely present in the pretrain stage, may disrupt the pretrained capabilities of VLAs. In addition, the inherently slow inference speed of VLAs hampers real-time responsiveness and limits the effective utilization of tactile feedback for action adjustment. To overcome these challenges, we propose Adaptive Tactile Vision-Language-Action (AT-VLA), which introduces a novel Adaptive Tactile Injection mechanism. This mechanism dynamically determines the appropriate timing and locations for tactile injection, incorporating only when it significantly contributes to action generation, thereby minimizing interference with pretrained representations. Furthermore, to enable rapid and accurate tactile responses, we propose a Tactile Reaction Dual-Stream mechanism, which decouples sensory processing into a slow visual-language stream for low-frequency perceptual reasoning and a fast tactile control stream for high-frequency physical interaction understanding, achieving real-time close-loop responses within 0.04 s. Real-world experiments thoroughly validate the effectiveness of AT-VLA in contact-rich manipulation tasks. The project page is available at: https://sites.google.com/view/at-vla.

The interaction of robots with bendable objects in midair presents significant challenges in control, often resulting in performance degradation and potential crashes, especially for aerial robots due to their limited actuation capabilities and constant need to remain airborne. This paper presents an adaptive controller that enables two aerial vehicles to collaboratively follow a trajectory while transporting a bendable object without relying on explicit elasticity models. Our method allows on-the-fly adaptation to the object's unknown deformable properties, ensuring stability and performance in trajectory-tracking tasks. We use Lyapunov analysis to demonstrate that our adaptive controller is asymptotically stable. Our method is evaluated through hardware experiments in various scenarios, demonstrating the capabilities of using multirotor aerial vehicles to handle bendable objects.

AI agents are increasingly deployed in multi-task settings, where the task to perform is specified at test time, and the agent must generalize to unseen tasks. A major concern in such settings is safety: often, an agent must not only execute unseen tasks, but do so while avoiding risks and handling ones that materialize. Empirical evidence suggests that even when the ability to execute generalizes to unseen tasks, the ability to do so safely frequently does not. This paper provides theory and experiments indicating that failures of agentic safety to generalize across tasks are not merely due to limitations of training methods, but reflect an inherent property of safety itself: the relationship between a task and its safe execution is more complex than the relationship between a task and its execution alone. Theoretically, we analyze linear-quadratic control with $H_{\infty}$-robustness, and prove that the mapping from task specification to an optimal controller has higher Lipschitz constant with safety requirements than without, yielding a Lipschitz bound of independent interest. Empirically, we demonstrate our conclusions in simulated quadcopter navigation with a neural network agent and in CRM with an LLM agent. Our findings suggest that current efforts to enhance agentic safety may be insufficient, and point to a need for fundamentally different approaches.

We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function $V_ψ$ whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint $\dot V_ψ+ αV_ψ\le 0$, projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41% on nominal friction and 24% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.

Adaptive control of Euler-Lagrange systems is challenging when friction is governed by a finite-horizon internal state that is not directly observable from joint measurements. In this setting, the measured closed-loop state is no longer Markovian, and standard certainty-equivalence adaptive laws may lose their convergence guarantees. The paper proposes a meta-control architecture in which the gains of a computed-torque controller are generated by a self-attention block processing a short window of recent motion history. The number of attention heads is selected before policy training through a surrogate analysis of the autocovariance of the memory-state gradient along the temporal window. This surrogate is based on a temporal adaptation of an incremental rank-tracking framework previously developed by the authors. The selected head count is then fixed and used as an architectural hyperparameter in a reinforcement-learning stage, where the policy is trained under a shielded admissibility constraint. The approach is tested on a 2-DOF manipulator with nonlinear friction and variable payload. In the short and matched memory regimes, the single-layer attention-only meta-controller outperforms a deeper Transformer baseline, with tracking-error reductions of 12 and 19 percentage points, respectively. The reported effect sizes are large, with d approximately -1.1 and -2.1, and Mann-Whitney p < 0.05 in both cases. In the long memory regime, however, the advantage disappears. Four out of ten training runs show either divergence or payload-invariant policy collapse, revealing a weakness in the static Phase-1 head-count prescription. This motivates moving rank-tracking inside the reinforcement-learning loop, allowing attention heads to be pruned or grown at runtime instead of fixed before training.

Many real-world problems require sequential decisions under uncertainty: when to inject or withdraw gas from storage, how to rebalance a pension portfolio each month, what temperature profile to run through a pharmaceutical reactor chain. Dynamic programming solves small instances exactly but scales exponentially in state dimensions. Black-box reinforcement learning handles high-dimensional states but trains slowly and produces no sensitivities. We introduce SNAPO (Smooth Neural Adjoint Policy Optimization), a framework that embeds a neural policy inside a known, differentiable simulator, replaces hard constraints with smooth approximations, and computes exact gradients of the objective with respect to all policy parameters and all inputs in a single adjoint pass. We demonstrate SNAPO on three domains: natural gas storage (training in under a minute, 365 forward curve sensitivities at no additional cost per sensitivity), pension fund asset-liability management (6.5x-200x sensitivity speedup over bump-and-revalue, scaling with the number of risk factors), and pharmaceutical manufacturing (cross-unit sensitivities through a 4-unit process chain, with 20 ICH Q8 regulatory sensitivities from 5 adjoint passes in 74.5 milliseconds). All sensitivities are produced by the same backward pass that trains the policy, at a cost proportional to one reverse pass regardless of how many sensitivities are computed.

Self-optimizing control is a strategy for selecting controlled variables, where the economic objective guides the selection and design of controlled variables, with the expectation that maintaining the controlled variables at constant values can achieve optimization effects, translating the process optimization problem into a process control problem. Currently, self-optimizing control is widely applied to steady-state optimization problems. However, the development of process systems exhibits a trend towards refinement, highlighting the importance of optimizing dynamic processes such as batch processes and grade transitions. This paper formally introduces the self-optimizing control problem for dynamic optimization, termed the dynamic self-optimizing control problem, extending the original definition of self-optimizing control. A novel concept, "dynamic controlled variables" (DCVs), is proposed, and an implicit control policy is presented based on this concept. The paper theoretically analyzes the advantages and generality of DCVs compared to explicit control strategies and elucidates the relationship between DCVs and traditional controllers. Moreover, this paper puts forth a data-driven approach to designing self-optimizing DCVs, which considers DCV design as a mapping identification problem and employs deep neural networks to parameterize the variables. Three case studies validate the efficacy and superiority of DCVs in approximating multi-valued and discontinuous functions, as well as their application to dynamic optimization problems with non-fixed horizons, which traditional self-optimizing control methods are unable to address.

Flapping-wing micro aerial vehicles offer quieter and safer operation than rotary-wing drones, yet achieving precise autonomous control of bird-scale ornithopters remains challenging: lift, airspeed, and turning authority are tightly coupled and governed by only a few control inputs. Conventional cascaded controllers treat altitude, speed, and heading independently, producing persistent tracking errors during complex maneuvers, while time-parameterized trajectory tracking requires predefined speed profiles that existing methods cannot robustly produce for these coupled dynamics. We address both limitations simultaneously with a Model Predictive Contouring Control (MPCC) approach that tracks arc-length-parameterized trajectories while optimizing progress online, eliminating the need for predefined timing. However, MPCC requires a dynamical model that captures the coupled aerodynamics without exceeding the computational budget of real-time nonlinear optimization. Here, we propose a compact, continuously differentiable model that captures the dominant couplings of bird-scale ornithopters, enabling real-time predictive control. We validated the method with the XFly ornithopter flying along circular and three-dimensional racing trajectories and achieved a mean deviation from the reference trajectory between 6.5 and 9 cm at speeds up to 3 m/s, which represents an almost 10-fold improvement over prior ornithopter control methods.

Instrumental variable (IV) and control function (CF) methods are powerful tools for causal effect estimation in the presence of unmeasured confounding, yet most existing approaches target only mean effects and/or demand substantial fitting and tuning effort. In this paper, we introduce a simple method, TabCF, for control function regression using tabular foundation models, which enables accurate, fast, identification-transparent, and tuning-light causal estimation of distributional quantities, such as interventional means and quantiles; we also propose a copula-based approximation for multivariate outcomes. TabCF performs favorably against representative methods across a broad range of small- to medium-sized synthetic and real data scenarios. The central message is two-fold: for practitioners, it highlights that TabCF is an effective tool for distributional causal inference; for researchers, it suggests that the proposed approach could be considered a strong baseline for future method development. Code is available at https://github.com/GepingChen/TabCF.

Tokamaks remain leading candidates for achieving practical fusion energy, yet many important control problems inside these devices are still difficult or unsolved. One such challenge is controlling the plasma rotation profile, which strongly influences stability, confinement, and transport. While the average rotation can be controlled, controlling the full profile is challenging due to high dimensionality, response to multiple actuators and dependence on plasma condition. Learning-based control methods, such as reinforcement learning (RL), provide a potential solution to this challenging problem with ability to model complex interactions leading to effective multi-input multi-output control. However, learning such policies is challenging due to the lack of accurate simulators that can model the rotation profile dynamics. In this work, we investigate the use of offline RL and offline model-based RL algorithms for rotation profile control, training them solely on historical data from the DIII-D tokamak. Our final method uses probabilistic models of plasma dynamics to generate rollouts for RL training. We deploy this policy on the DIII-D Tokamak and observe promising real-world results. We conclude by highlighting key challenges and insights from training and deploying an RL policy on a complex physical device while using only limited past data.

Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a computationally intractable problem. Therefore, approaches that can guarantee safety while reducing conservatism will help improve the optimality of the system under consideration. Here, we present a Model Predictive Control (MPC) formulation using CBF as a terminal constraint, which is proven to improve feasibility and reachable sets with increasing prediction horizon. The constructive nature of the proofs allows for warm-starting the nonlinear optimization problem, thereby reducing the computational time substantially. Simulations are set up for a simple nonholonomic system to numerically validate the results, and it is observed that the number of infeasible points decreased by a factor of 1.7 to 2.7. The increase in reachable state space was demonstrated by the ability of the system to track trajectories that are entirely inside the unsafe region of the control barrier function.

Generative models based on static scalar energy functions represent an emerging paradigm in which a single time independent potential drives sample generation through its gradient field, eliminating the need for time conditioning entirely. We unify the training and sampling phases of this paradigm, conventionally treated as separate procedures, within a single framework: density transport on the Wasserstein space, cast as a nonlinear control problem in which the Kullback Leibler (KL) divergence serves as a Lyapunov function. Training and sampling are then two instances of this same master dynamics, differing only in initial condition. Within this autonomous framework we develop two analytic results. First, since the Lyapunov certificate is asymptotic, we derive a finite step stopping criterion for Langevin sampling and prove that no Lyapunov certificate exists for the deterministic gradient flow on the same energy landscape. Second, the reformulation brings the toolkit of nonlinear control theory to bear on static scalar energy generative modeling, that is, we show that additive composition of trained scalar energies retains an explicit Gibbs invariant measure and inherits the closed-loop Lyapunov certificate. Beyond these immediate results, this reformulation bridges static scalar energy generative models with the full toolkit of nonlinear control theory, opening the door to barrier functions for constrained generation and contraction metrics for accelerated sampling. Experiments on synthetic distributions validate the theoretical predictions.

This paper presents a subsystem-based adaptive control framework for serial flexible manipulators with an arbitrary number of links, in which the elastic deformation PDE of each link is carried through the entire control design without spatial discretization or modal truncation. All dynamic quantities -- rigid-body motion, elastic deformation, and inter-link constraint forces -- are expressed uniformly as body-fixed twists and wrenches within the se3 Lie-algebraic structure. A controllable form of the per-link dynamics is derived by substituting the strain-based deformation PDE into the dynamic equation, eliminating distributed elastic acceleration and yielding a model governed by the body-fixed twist acceleration and deformation field. Desired subsystem twist trajectories are generated via a deflection-compensating inverse kinematics procedure. A nominal per-link controller is proven to produce exponential twist error decay via a per-subsystem Lyapunov function. An adaptive modification replaces exact physical parameters with online estimates governed by a projection-based law, augmenting with a parameter estimation error term. Upon summing over all links, the interaction power terms telescope to zero by Newton's third law and the frame invariance of the natural power pairing on se3se(3), establishing exponential convergence of all twist errors and bounded elastic deformation under both nominal and adaptive controllers. The screw-theoretic structure renders interaction term cancellation exact, making the stability certificate modular and scalable to chains of arbitrary length. The framework is validated numerically on a two-link flexible manipulator in three-dimensional motion.

Abrupt cable severance in multi-UAV slung-load transport redistributes load and changes the active constraint set, leaving limited time for fault diagnosis and reconfiguration. Existing controllers rely on coordinated force allocation, peer-state exchange, or fixed cable topology, and therefore lack a certified decentralized recovery mechanism for unannounced severance. We present a passive architecture that routes each vehicle's measured cable tension directly into its altitude thrust command, $T_i^{\mathrm{ff}}=T_i$, while a surrounding proportional-derivative, anti-swing, and projection cascade preserves local tracking feasibility. The main contribution is a conditional hybrid practical input-to-state-stability certificate that composes a slack-excursion-bounded taut-cable reduction, bounded post-severance Lyapunov jumps, inter-fault decay, and per-fault-cycle contraction $ρ\in (0,1)$ into an explicit recovery envelope under stated actuator, slack, and dwell assumptions. We validate the controller in Drake multibody simulation with five vehicles, a 10 kg payload, Kelvin-Voigt cables, Dryden wind, and single- and dual-severance schedules: the closed loop attains 0.312-0.328 m RMSE, 76.1-95.2 mm peak sag, and recovery within one payload-pendulum period. Disabling the identity inflates cruise error by 34-39% and peak sag by 3.6x-4.0x, identifying local tension feed-forward as the dominant passive recovery mechanism in the tested decentralized cascade.

We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy may rely on the full phase-space state, practical feedback is typically limited to sparse macroscopic diagnostics. We therefore study imitation learning methods that distill a fully observed expert policy into controllers operating only on macroscopic measurements. We show the stability guarantees of the learned policy, where the error floor depends on the minimal behavior cloning loss achievable under the observation constraints. We further characterize this minimal loss in terms of a notion of entropy that quantifies the complexity of the initial distribution. Our results demonstrates the theoretical feasibility of learning stabilizing feedback policies for kinetic plasma dynamics from macroscopic observations, and exhibits the adaptivity of the learning approach to low-complexity structures. Through extensive numerical experiments, we validate our theory and show that the learned policies can stabilize the system using only macroscopic observations, within a significantly longer time horizon than non-adaptive baseline controllers.

Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, particularly under time-varying conditions and under stale-plan execution. We propose Bilinear Mamba-Koopman Neural MPC, a minimal extension that introduces control-dependent coupling in the latent dynamics, allowing the effective operator to adapt to the current input. The resulting model is a strict generalization of the standard linear, conditional-independence formulation, adds less than 1% parameters through a low-rank structure, and admits exact model Jacobians that enable efficient Sequential Convex Programming (SCP) with monotone-descent and KKT convergence results under standard trust-region assumptions. Across CartPole and RSCP benchmarks in time-invariant and time-varying regimes, the proposed model matches or improves forecasting accuracy on every cell when training noise is averaged out, with strict gains where control-state coupling is structurally present. Its main closed-loop gains appear in the RSCP TV task, where iterative SCP improves adaptation within the horizon and substantially stabilizes training; in CartPole TV, the gains are modest but consistent. In delayed re-planning experiments on the time-varying variants, the bilinear model degrades more gracefully under stale-plan execution, maintaining a consistent advantage on CartPole TV and a substantially larger robustness margin on RSCP TV. These results show that control-dependent latent dynamics provide a simple and effective mechanism for robust MPC under varying conditions.

A central challenge of visual control with model-based reinforcement learning (RL) is reliable long-horizon planning: long rollouts with learned latent dynamics exhibit branching futures and multi-modal action-value distributions. In addition, compounding model errors amplified by visual occlusions make deep imagination brittle. We present ELVIS, a latent model predictive controller (MPC) designed to make long-horizon planning practical. ELVIS plans in a Dreamer-style recurrent state space model (RSSM) and replaces standard unimodal model predictive path integral (MPPI) with a Gaussian-mixture MPPI that maintains multiple coherent hypotheses over long horizons, avoiding mode averaging under branching rollouts. In parallel, ELVIS stabilizes deep imagination with a shared uncertainty-aware lambda-return: an ensemble of latent critics defines an upper-confidence-bound (UCB) score that gates a time-varying lambda, adaptively trading off bootstrapping versus look-ahead to limit compounding error during planning. The same return is used both to train an actor-critic prior from imagined rollouts and to score candidate trajectories inside GMM-MPPI, aligning RL objectives with the planner's long-horizon optimization. On fourteen DeepMind Control Suite visual tasks, ELVIS establishes state-of-the-art performance compared with TD-MPC2 and DreamerV3. Finally, ELVIS transfers zero-shot to a real-world sand-spraying task with severe occlusions, improving surface-quality metrics and demonstrating robustness beyond simulation.

This paper presents a multi-phase whole-body model predictive control (MPC) approach for bipedal walking, combining a detailed whole-body model in the near horizon with a simplified single-rigid-body model in the later prediction steps. This reduces computational complexity while retaining prediction capabilities. The resulting nonlinear optimal control problem is solved entirely within the general-purpose, off-the-shelf nonlinear MPC framework acados, using sequential quadratic programming (SQP). Given a contact schedule and a target walking speed, the controller optimizes joint torques without depending on preselected footstep locations. The controller is validated in MuJoCo simulation on the 18-DoF bipedal robot HyPer-2.

State-of-the-art model-based Reinforcement Learning (RL) approaches either use gradient-free, population-based methods for planning, learned policy networks, or a combination of policy networks and planning. Hybrid approaches that combine Model Predictive Control (MPC) with a learned model and a policy prior to leverage the advantages of both paradigms have shown promising results. However, these approaches typically rely on gradient-free optimization methods, which can be computationally expensive for high-dimensional control tasks. While gradient-based methods are a promising alternative, recent works have empirically shown that gradient-based methods often perform worse than their gradient-free counterparts. We propose Dream-MPC, a novel approach that generates few candidate trajectories from a rolled-out policy and optimizes each trajectory by gradient ascent using a learned world model, uncertainty regularization and amortization of optimization iterations over time by reusing previously optimized actions. Our results on 24 continuous control tasks show that Dream-MPC can significantly improve the performance of the underlying policy and can outperform gradient-free MPC and state-of-the-art baselines. Code and videos are available at https://dream-mpc.github.io.

Post-training large language models (LLMs) often suffers from catastrophic forgetting, where improvements on a target objective degrade previously acquired capabilities. Recent evidence suggests that this phenomenon is primarily driven by excessive distributional drift during optimization. Motivated by this perspective, we propose Anchored Learning, a simple framework that explicitly controls distributional updates during offline fine-tuning via a dynamically evolving moving anchor. Instead of matching a fixed reference distribution, the anchor interpolates between the current model and a frozen reference to construct an intermediate target that the model distills toward, transforming global fine-tuning into a sequence of local trust-region updates in distribution space. Theoretically, we prove this anchor-based update admits a linear KL-divergence upper bound per iteration, ensuring a stable transition between model distributions. Extensive experiments on iGSM, MedCalc, and IFEval show that Anchored Learning consistently lies on the Pareto frontier of gain-stability trade-offs, achieving near-optimal performance improvements while substantially reducing degradation compared to strong baselines. For example, while standard SFT suffers from over 53% performance degradation on iGSM and MedCalc, Anchored Learning slashes this drop to under 5% while maintaining near-optimal gains (e.g., 75.2% on iGSM).

In this article, we study unbalanced optimal transport (UOT) and establish a control-theoretic dynamical extension, which we call the unbalanced density control (UDC), for a class of Gaussian reference measures. In the static setting, we consider UOT with quadratic transport cost and Kullback--Leibler penalties on the marginals relative to prescribed Gaussian measures. We show that the infinite-dimensional variational problem admits an exact Gaussian reduction, yielding a finite-dimensional optimization over masses, means, and covariances, together with a closed-form expression for the optimal transported mass. We then formulate UDC for discrete-time linear systems, where the initial and terminal state measures are imposed softly through KL penalties and the intermediate evolution is governed by controlled linear dynamics with quadratic control cost. For this problem, we prove that any feasible solution can be replaced, without loss of optimality, by a Gaussian initial measure and an affine-Gaussian control policy. This leads to an exact finite-dimensional reformulation and, after a standard covariance-steering lifting, to an SDP-based optimization for fixed mass, again coupled with a closed-form mass update. We further establish existence of optimal solutions and identify a sufficient condition under which the affine-Gaussian UDC policy is deterministic. These results provide globally optimal solution methods for both Gaussian UOT and Gaussian UDC. Finally, we illustrate our results with several numerical examples.

Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often discarding cross-layer interactions induced by the network computation. We introduce Layerwise LQR (LLQR), a framework for learning structured inverse preconditioners under a global layerwise optimal-control objective. The starting point is an exact equivalence: the steepest-descent step under a broad class of divergence-induced quadratic models--including Newton, Gauss-Newton, Fisher/natural-gradient, and intermediate-layer metrics--can be written as a finite-horizon Linear Quadratic Regulator (LQR) problem. This formulation serves as a reference that exposes the layerwise dynamics and cost matrices encoding the original dense geometry. We then derive a scalable relaxation that learns diagonal, (E-)Kronecker-factored, or other structured inverse preconditioners by minimizing the LQR objective and reusing them across iterations. The resulting optimizer wraps standard methods while retaining a principled connection to second-order geometry, without forming or inverting the global curvature matrix. Experiments on ResNets and Transformers show that LLQR improves optimization dynamics and often translates these gains into improved final test performance, while adding only modest wall-clock overhead. It establishes LLQR as a practical framework for geometry-aware second-order methods and a reference for evaluating scalable approximations.

Real-world control systems must achieve long-horizon objectives (liveness) while respecting continuous-time safety constraints, a combination that motivates hierarchical layered control architectures (LCAs). Existing LCA research, however, lacks (i) a uniform specification language across discrete planning and continuous execution, (ii) formal guarantees that specifications are preserved when interconnecting subsystems at heterogeneous time scales, and (iii) compositional separation between layers, owing to reliance on naive input-filtering laws. This paper addresses all three gaps by importing the safety--liveness decomposition into a heterogeneous assume--guarantee framework: \emph{safety is enforced by invariance} at the continuous-time layer, while \emph{liveness is achieved through refinement} at the discrete-time layer, with inter-layer coordination formalized via vertical refinement and timing-compatibility conditions. We instantiate this contract with a novel LCA combining an MPC planner, an input-to-state stabilizing (ISS) low-level controller, and a reference-governor bridge, and validate it on a Hybrid Energy Storage System (HESS) comprising a battery and a supercapacitor.

We study scalar dyadic refinement operators on R^2 of the form (Vf)(x,y) = sum_{(j,k) in Z^2} c_{j,k} f(2x-j, 2y-k), where only finitely many mask coefficients c_{j,k} are nonzero. Under a fixed support-window hypothesis, we prove that for every compactly supported continuous piecewise linear seed g:R^2->R, the iterates V^n g admit exact ReLU realizations of fixed width and depth O(n). This gives a first genuinely two-dimensional extension of the exact realization theory for refinement cascades. Using the one-dimensional exact loop-controller framework, the proof transports the tensor-product residual dynamics exactly on the product of two polygonal loops and reduces the remaining seam ambiguity to a final readout and selector step. The matrix cascade is then handled by a fixed-depth recursive block, and general compactly supported continuous piecewise linear seeds are reduced to a finite decomposition together with exact clamped gluing on the support window. This identifies the tensor-product dyadic case as a natural first multivariate instance of the loop-controller method for refinement iterates.

Contextual MDPs are powerful tools with wide applicability in areas from biostatistics to machine learning. However, specializing them to offline datasets has been challenging due to a lack of robust, theoretically backed methods. Our work tackles this problem by introducing a new approach towards adaptive estimation and cost optimization of contextual MDPs. This estimator, to the best of our knowledge, is the first of its kind, and is endowed with strong optimality guarantees. We achieve this by overcoming the key technical challenges evolving from the endogenous properties of contextual MDPs; such as non-stationarity, or model irregularity. Our guarantees are established under complete generality by utilizing the relatively recent and powerful statistical technique of $T$-estimation (Baraud, 2011). We first provide a procedure for selecting an estimator given a sample from a contextual MDP and use it to derive oracle risk bounds under two distinct, but nevertheless meaningful, loss functions. We then consider the problem of determining the optimal control with the aid of the aforementioned density estimate and provide finite sample guarantees for the cost function.

Continuous-memory recurrent networks must preserve phase, position, or orientation despite model imperfections and state noise. We develop a geometric framework that separates three questions: how many memory coordinates are neutrally transported, how deterministic perturbations alter their finite-horizon stability, and how ambient noise is decoded along them. Exact per-input equivariance transports analytical group tangents pathwise and, on a compact nondegenerate orbit stratum, yields at least $q=\dim(G/H)$ zero group-tangent Lyapunov exponents under stationary ergodic driving. For imperfect dynamics, a four-block tangent/normal decomposition gives local and finite-horizon bounds on tangent growth and subspace rotation, distinguishing first-order direct damage from second-order leakage through contracting normal directions. For noisy dynamics, a specified decoder maps ambient covariance $Q$ to coordinate covariance $ZQZ^\top$; under isotropic noise and fixed tangent energy, least-squares decoding and scaled-isometric action geometry minimize local diffusion. Local and finite-horizon evaluations include cases both within and outside the sufficient conditions. In a fresh twenty-seed $T^2$ replication, a decoder-covariance objective improves noisy horizon-256 memory in every pair while meeting a prespecified clean-error equivalence margin. Direct noise training also improves noisy memory but incurs a clean-error tradeoff. In coupled $T^4/T^8$ integrators, the advantage of anisotropic-covariance over isotropic regularization reverses when evaluation noise becomes isotropic. These results connect continuous symmetry to measurable limits and design choices for recurrent memory under explicit dynamical, decoder, and noise assumptions.

Domain randomization (DR) is widely used in policy learning to improve robustness to modeling error, but remains underexplored in contact-rich sampling-based predictive control (SPC), where rollout quality is highly sensitive to uncertainty. In this work, we take the first step by studying risk-aware DR in predictive sampling on a simple yet representative Push-T task, comparing average, optimistic, and pessimistic rollout aggregations under randomized model instances. Our initial results suggest that DR affects not only robustness to model error, but also the effective cost landscape seen by the sampling-based optimizer, by reshaping the basin of attraction around contact-producing actions. This opens up potential for exploring better grounded risk-aware contact-rich SPC under model uncertainty. Video: https://youtu.be/f1F0ALXxhSM

Many physical AI tasks require sequential implicit computation: at each step, boundary controls are applied, and the resulting configuration is obtained by solving an equilibrium problem. This setting arises naturally in deformable object manipulation, where even bending a deformable linear object (DLO) to a target shape can be nonlinear and multistable: identical boundary conditions may produce different configurations depending on actuation history. Unlike explicit transition models, the control-to-configuration relation is implicit and history-dependent, making long-horizon learning and control brittle; backpropagating through iterative solves is also memory- and compute-intensive. We propose Neural Control, a boundary-control framework that propagates gradients through branch-dependent sequences of equilibrium solves rather than a single fixed point. Neural Control computes trajectory-dependent proxy gradients by differentiating equilibrium conditions with an adjoint formulation, avoiding solver unrolling while keeping forward rollouts on converged equilibria. Combined with receding-horizon continuation, Neural Control re-anchors optimization to realized equilibria and mitigates basin switching. We validate Neural Control on simulated and real DLO manipulation, compare against SPSA and iCEM, and demonstrate applicability to a learned DEQ-style implicit equilibrium model.

Model Predictive Path Integral (MPPI) control is a powerful sampling-based strategy for nonlinear autonomous systems. However, its performance is often bottlenecked by the fidelity of nominal dynamics. We propose ICODE-MPPI, a robust framework that leverages Input Concomitant Neural Ordinary Differential Equations (ICODEs) to learn and compensate for unmodeled residual dynamics. Unlike discrete-time learners, ICODEs maintain physical consistency and temporal continuity during the MPPI prediction horizon. High-fidelity simulations on complex trajectories demonstrate that ICODE-MPPI achieves up to a 69% reduction in cross-tracking error under persistent disturbances compared to standard MPPI control. Furthermore, our analysis confirms that ICODE-MPPI significantly suppresses control chattering, yielding smoother steering commands and superior robust performance.

Autonomous driving technology has rapidly evolved over the past decade, offering significant improvements in transportation efficiency, safety, and cost reduction. While much of the progress has focused on highway driving and obstacle avoidance, low-speed maneuvers such as parking remain among the most difficult challenges for autonomous systems. This challenge is especially pronounced in trailer-truck transport vehicles due to their articulated motion and environmental constraints. This paper presents a proposed framework for autonomous truck parking that integrates perception, motion planning, control systems, and infrastructure awareness. By combining sensor fusion, Hybrid A* path planning, nonlinear model predictive control (NMPC), and data-driven parking systems, this work highlights the importance of system-level coordination for reliable and scalable autonomous parking solutions. As a proof-of-concept implementation, we adapted an open-source A* path planning simulation to incorporate a tractor-trailer kinematic model, demonstrating articulated vehicle path planning within a command-line simulation environment, with jackknife prevention identified as an area requiring further development.

This paper presents a novel model predictive control (MPC) approach for autonomous pick-and-place between moving platforms with a hook-equipped aerial manipulator. First, for accurate and rapid modeling of the complex dynamics, a digital twin model of the quadcopter equipped with a hook-based gripper, implemented in MuJoCo, is constructed and used as the predictive model for the MPC. To handle uncertainties of the predictive model (e.g. due to aerodynamics and uncertain payloads), a robust adaptive MPC approach is proposed. By systematic integration of zero-order robust optimization (zoRO) based uncertainty propagation and an extended Kalman filter (EKF) for parameter estimation, the MPC algorithm ensures robust constraint satisfaction, high performance, and computational efficiency. The effectiveness of the proposed method is evaluated in complex simulated scenarios and in real-world flight experiments.

We study feedback motion planning for continuous-time stochastic nonlinear systems under signal temporal logic (STL) specifications. We propose a framework that synthesizes control policies for chance-constrained STL trajectory optimization problems, with the goal of ensuring that the closed-loop stochastic system satisfies a given STL formula with high probability (e.g., 99.99%). Our approach is based on a predicate erosion strategy that transforms the intractable stochastic problem into a deterministic STL trajectory optimization problem with tightened STL formula constraints. The amount of erosion is determined by a probabilistic reachable tube (PRT) that bounds the deviation between the stochastic trajectory and an associated nominal trajectory. To compute such bounds, we leverage contraction theory and feedback design, and develop several tracking controllers. This yields a complete feedback motion planning pipeline which can be implemented by numerical optimizations. We demonstrate the efficacy and versatility of the proposed framework through simulations on several robotic systems and through experiments on a real-world quadrupedal robot, and show that it is less conservative and achieves higher specification satisfaction probability than representative baselines.